To find the equation of the square root function after all the transformations, we can start with the general form of a square root function:

$y = \sqrt{x}$

Now, let's apply each transformation step-by-step:

1. Shift 5 units up: This affects the vertical position of the graph. We add 5 to the function: $y = \sqrt{x} + 5$

2. Shift 6 units right: Shifting a graph to the right involves replacing $x$ with $x - 6$. This modifies the function as follows: $y = \sqrt{x - 6} + 5$

3. Horizontal stretch by a factor of 9: A horizontal stretch by a factor of $k$ involves replacing $x$ with $x / k$. Here, $k = 9$, so we replace $x$ with $x / 9$: $y = \sqrt{\frac{x}{9} - 6} + 5$

4. Reflect over the y-axis: Reflecting over the y-axis means we replace $x$ with $-x$: $y = \sqrt{\frac{-x}{9} - 6} + 5$

Thus, the final equation after all the transformations is:

$y = \sqrt{\frac{-x}{9} - 6} + 5$

---

Would you like more clarification or details on any of the transformations? Here are a few related questions that could expand your understanding:

1. How do horizontal stretches and compressions affect the graph of a function?
2. What is the effect of reflecting a function over the y-axis in general?
3. How would shifting a square root function down or left change the equation?
4. Can you explain the difference between vertical and horizontal shifts in terms of function transformations?
5. How would you write the equation for a square root function that is reflected over the x-axis instead of the y-axis?

Tip: To easily visualize function transformations, try graphing the function step by step using a graphing calculator or software to see the changes as you apply each transformation.